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%I
%S 2,3,12,10,30,21,56,36,90,55,132,78,182,105,240,136,306,171,380,210,
%T 462,253,552,300,650,351,756,406,870,465,992,528,1122,595,1260,666,
%U 1406,741,1560,820,1722,903,1892,990,2070,1081,2256,1176,2450,1275,2652,1378
%N Denominator of (n+2)/(n*(n+1)).
%H G. C. Greubel, <a href="/A168059/b168059.txt">Table of n, a(n) for n = 1..1000</a>
%F From _R. J. Mathar_, Nov 18 2009: (Start)
%F a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
%F G.f.: x*(2+3*x+6*x^2+x^3)/((1-x)^3*(1+x)^3).
%F a(2n+1) = A002939(n+1).
%F a(2n) = A014105(n). (End)
%F a(n) = lcm(n+1, binomial(n+1,2)). - _Enrique Pérez Herrero_, Mar 13 2012
%F From _Ilya Gutkovskiy_, Jul 08 2016: (Start)
%F E.g.f.: x*(x + 1)*sinh(x) + x*(x + 4)*cosh(x)/2.
%F a(n) = n*(n + 1)*(3 - (-1)^n)/4.
%e a(4)=10 because 6/(5*4) = 3/10 has 10 in the denominator.
%t Table[Denominator[(n+2)/(n+1)/n],{n,60}]
%o (PARI) a(n) = denominator((n+2)/(n*(n+1))); \\ _Michel Marcus_, Jul 09 2016
%o (MAGMA) [Lcm(n+1, Binomial(n+1,2)): n in [1..60]]; // _Vincenzo Librandi_, Mar 13 2018
%Y Numerator is in A026741.
%K nonn,frac,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Nov 17 2009
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